# Additive Tree Distances

### Description

Objects representing additive tree distances.

### Usage

1 |

### Arguments

`x` |
an R object representing additive tree distances. |

### Details

Additive tree distances are object dissimilarities *d* satisfying
the so-called *additive tree conditions*, also known as
*four-point conditions* *d_{ij} + d_{kl} ≤ \max(d_{ik} +
d_{jl}, d_{il} + d_{jk})* for all quadruples *i, j, k, l*.
Equivalently, for each such quadruple, the largest two values of the
sums *d_{ij} + d_{kl}*, *d_{ik} + d_{jl}*, and *d_{il} +
d_{jk}* must be equal.
Centroid distances are additive tree distances where the inequalities
in the four-point conditions are strengthened to equalities (such that
all three sums are equal), and can be represented as *d_{ij} = g_i
+ g_j*, i.e., as sums of distances from a “centroid”.
See, e.g., Barthélémy and Guénoche (1991) for more details on additive
tree distances.

`as.cl_addtree`

is a generic function. Its default method can
handle objects representing ultrametric distances and raw additive
distance matrices. In addition, there is a method for coercing
objects of class `"phylo"`

from package
ape.

Functions `ls_fit_addtree`

and
`ls_fit_centroid`

can be used to find the additive tree
distance or centroid distance minimizing least squares distance
(Euclidean dissimilarity) to a given dissimilarity object.

There is a `plot`

method for additive tree distances.

### Value

An object of class `"cl_addtree"`

containing the additive
tree distances.

### References

J.-P. Barthélémy and A. Guénoche (1991).
*Trees and proximity representations*.
Chichester: John Wiley & Sons.
ISBN 0-471-92263-3.

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